In a nonreactive stockpot, combine the brine ingredients with enough water to cover the pork (about 8 1/2 cups, 2 liters). Bring to a boil, then remove from the heat and let cool completely. Add the pork to the pot, and refrigerate for at least 12 hours or up to 24 hours.
Once the pork has brined, preheat the oven to 275˚F (135˚C). Remove the pork from the brine, patting it dry with paper towels, and cut it into 2 inch (5 cm) pieces.
In a large Dutch oven, heat the fat over medium heat until it melts. Add the pork pieces, cover the pot, and roast in the oven until the meat is very tender, about 2 hours. Transfer the meat to a mixing bowl, discarding the oil. Finely chop the chipotles and add them to the meat with their sauce. Add the orange and lime juice, toss to combine, and season with salt and pepper to taste.
To assemble, spread each tortilla with crema, if using, and top with a generous amount of the seasoned pork. Sprinkle with the pickled onions and jalapeños, if using, and top with the cucumber slices, cilantro, and a squeeze of fresh lime.